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2 months ago

According to this diagram, what is tan 62 degrees ?

Mathematics

2 answers:

Svet_ta [12.7K]2 months ago

7 0

Response:

$tan62^{\circ}=1.875$

Detailed explanation:

We know that

the length of the perpendicular side of the right triangle is 15 units

the base of the right triangle measures 8 units

the hypotenuse measures 17 units

We need to determine the value of $tan62^{\circ}$

From our knowledge

$tan\theta=\frac{Perpendicular\;side}{Base}$

Substituting the values gives us

$tan62^{\circ}=\frac{15}{8}=1.875$

Thus, the resulting value of $tan62^{\circ}=1.875$

PIT_PIT [12.4K]2 months ago

3 0

Refer to the image below

if you want to understand how to identify opposite or adjacent sides; notice that if you look directly at the angle, you will see the side opposite to it, while the adjacent side is the one that touches the angle.

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A high school basketball player attempted 35 free throws in a season. An analyst determined that the player successfully made 4

zzz [12365]

36 divided by 6
which results in 6
then multiply 6 x 5
which gives 30

your final answer is: 30

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8 0

1 month ago

The mass of a colony of bacteria, in grams, is modeled by the function P given by P(t)=2+5tan^−1.(t/2), where t is measured in d

AnnZ [12381]

Answer:

1.21 g/day

Step-by-step explanation:

We start with the fact that

The mass of the bacterial colony (in grams) is described by

$P(t)=2+5tan^{-1}(\frac{t}{2})$

Where t=Time(in days)

Next, we differentiate with respect to t

$P'(t)=5(\frac{1}{1+\frac{t^2}{4}}\times \frac{1}{2})$

Using the formula $\frac{d(tan^{-1}(x)}{dx}=\frac{1}{1+x^2}$

$P'(t)=\frac{5}{2}(\frac{4}{4+t^2})$

$P'(t)=\frac{10}{4+t^2}$

We know that P(t)=6

Now, substitute this value

$6=2+5tan^{-1}(\frac{t}{2})$

$5tan^{-1}(\frac{t}{2})=6-2=4$

$tan^}{-1}(\frac{t}{2})=\frac{4}{5}$

$\frac{t}{2}=tan(\frac{4}{5})$

$t=2tan(\frac{4}{5})$

Insert the given value of t

$P'(2tan\frac{4}{5})=\frac{10}{4+4tan^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{10}{4}\times \frac{1}{1+tan^2(\frac{4}{5})}$

We understand that $1+tan^2\theta=sec^2\theta$

Applying the formula

$P'(2tan(\frac{4}{5})=\frac{5}{2}\times \frac{1}{sec^2(\frac{4}{5})}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times cos^2(\frac{4}{5})$

By employing $cos^2x=\frac{1}{sec^2x}$

$P'(2tan\frac{4}{5})=\frac{5}{2}\times (0.696)^2=1.21$ g/day

Consequently, the instantaneous rate at which the mass of the colony changes is=1.21g/day

7 0

3 months ago

Read 2 more answers

Ralph has budgeted $175 for entertainment. He uses this money to go out on dates for $35 or to go out with his friends for $15.

AnnZ [12381]

If Ralph allocated $180 rather than the intended $175 for entertainment, he spent $35 for each date and let's denote "x" as the number of dates he attended. He also spent $15 when going out with friends, where "y" represents his outings with friends.

The accurate equation is "B" which is 35x + 15y = 180.

8 0

2 months ago

USING STRUCTURE An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles, as s

AnnZ [12381]

Answer:

Step-by-step explanation:

Refer to the attached digram.

The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.

The perimeter of a rectangle can be expressed as 2(x+r) where:

x is the length

2r represents the rectangle's width, equivalent to the semicircle's diameter.

The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.

Thus, the total perimeter contributed by the two semicircles is 2πr.

Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr

where r indicates the semicircle's radius.

Expanding this gives us

Perimeter of the track = 2x + 4r + 2πr

which can also be represented as Perimeter of the track = 2(x + 2r + πr)

b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.

P = 2x + 4r + 2πr

By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x

Next, we divide each side by 2.

(P - 4r - 2πr) / 2 = 2x

Thus, x = (P - 4r - 2πr) / 2

c) Given

P = 600ft

r = 50ft

x = (600 - 4(50) - 2π(50)) / 2

x = (600 - 200 - 100(3.14)) / 2

x = 400 - 314 / 2

x = 86 / 2

x = 43ft

Therefore, rounding to the nearest foot, the value of x is 43ft

4 0

2 months ago

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function? y = –3x y = –y e

tester [12383]

Response:

The function is represented by the equation,

x = 3y.

Detailed explanation:

The direct variation function includes the points (-9, -3) and (-12, -4).

Here,

$\frac {-9}{-3} = \frac {-12}{-4}$ = 3

Thus, the function can be expressed as,

x = 3y.

6 0

2 months ago

Read 2 more answers