All categories

6 days ago

What is the value of y in the formula shown when x = 4/5?

Mathematics

1 answer:

Leona [9.2K]6 days ago

6 0

4(4/5) + √(4/5) + 0.2 - 5(4/5)

= 16/5 + (2√5/5) + (1/5) - 4

= (16 + 2√5 + 1 - 20)/5

= (2√5 - 3)/5 or 0.29442719

You might be interested in

one day, the state fair total attaendance was 126,945. Round to the nearest hundred thousand, nearest ten thousand and nearest t

zzz [9080]

Nearest hundred thousand: 100,000

Nearest ten thousand: 130,000

Nearest thousand: 127,000

The amount that is closest to the actual attendance is 127,000 when rounded to the nearest thousand.

6 0

1 month ago

Read 2 more answers

Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.

Svet_ta [9500]

Answer:

x=9,-1 and $x^2+(-8)x=9$

Explanation:

We are given the quadratic equation $x^2-8x-9$

, which we then compare with the standard form of a quadratic. The general quadratic is identified as $ax^2+bx+c=0$

. From our given equation, it follows that a=1,b=-8,c=-9

. To calculate the discriminant, we insert these values into the formula $D=b^{2}-4ac$

$D=(-8)^2-4(1)(-9)=100$

. Now, to find the value of x

The formula is $x=\frac{-b\pm\sqrt{D}}{2a}$

. The resulting equation will be obtained by rewriting the original equation through rearranging 9 to the right side and applying negative signs within brackets to convert the expression into the form of

$x^2+bx=c$

4 0

7 days ago

Read 2 more answers

If SA=1/2lp+B, find p<br><br> What is the formula for finding p?

Svet_ta [9500]

<span>To isolate p, start by subtracting B from both sides: SA-B=1/2lp. Next, multiply both sides by 2 to eliminate the 1/2: 2SA=lp. Finally, divide both sides by l to derive p: (2SA)/l=p.</span>

8 0

1 month ago

Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Leona [9271]

Response-

(78,104) represents the point closest to the interior.

Explanation-

The equation defining the circle,

$\Rightarrow x^2+y^2 = 16900$

$\Rightarrow y^2 = 16900-x^2$

$\Rightarrow y = \sqrt{16900-x^2}$

Since the point lies on the circle, its coordinates must be,

$(x,\sqrt{16900-x^2})$

The distance "d" from the point to (30,40) can be calculated as,

$=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$=\sqrt{(x-30)^2+(\sqrt{16900-x^2}-40)^2}$

$=\sqrt{x^2+900-60x+16900-x^2+1600-80\sqrt{16900-x^2}}$

$=\sqrt{9400-60x-80\sqrt{16900-x^2}}$

Next, we need to determine the value of x for which d is minimized. The minimum distance occurs when $9400-60x-80\sqrt{16900-x^2}$ is at its lowest value.

Let’s set up the equation,

$\Rightarrow f(x)=9400-60x-80\sqrt{16900-x^2}$

$\Rightarrow f'(x)=-60+80\dfrac{x}{\sqrt{16900-x^2}}$

$\Rightarrow f''(x)=\dfrac{1352000}{\left(16900-x^2\right)\sqrt{16900-x^2}}$

We find the critical points,

$\Rightarrow f'(x)=0$

$\Rightarrow-60+80\dfrac{x}{\sqrt{16900-x^2}}=0$

$\Rightarrow 80\dfrac{x}{\sqrt{16900-x^2}}=60$

$\Rightarrow 80x=60\sqrt{16900-x^2}$

$\Rightarrow 80^2x^2=60^2(16900-x^2)$

$\Rightarrow 6400x^2=3600(16900-x^2)$

$\Rightarrow \dfrac{16}{9}x^2=16900-x^2$

$\Rightarrow \dfrac{25}{9}x^2=16900$

$\Rightarrow x=\sqrt{\dfrac{16900\times 9}{25}}=78$

$\Rightarrow x=78$

Then,

$\Rightarrow f''(78)=\dfrac{1352000}{\left(16900-78^2\right)\sqrt{16900-78^2}}=\dfrac{125}{104}=1.2$

Since f''(x) is positive, the function f(x) achieves its minimum at x=78

When x is set to 78, the corresponding y value will be

$\Rightarrow y = \sqrt{16900-x^2}=\sqrt{16900-78^2}=104$

This leads us to conclude that the closest point is (78,104)

5 0

1 month ago

Maggie is considering two investments. Investment A Investment B Principal $10,000 $8,000 Interest rate 3% 2.8% Time in years 5

Zina [9171]

To determine this, we will apply the simple interest formula: $A=P(a+rt)$
where
$A$ signifies the total amount.
$P$ indicates the principal amount.
$r$ represents the interest rate in decimal.
$t$ denotes the time period in years.

Investment A. The initial investment amount is $10,000, so $P=10000$ . The investment period is 5 years, meaning $t=5$ . To express the interest rate in decimal, divide it by 100%
$r= \frac{3}{100} =0.03$
Now, we can substitute these values into our formula to find $A$ :
$A=P(a+rt)$
$A=10000(1+0.03*5)$
$A=11500$

Investment B. $P=8000$ , $t=15$ , and $r= \frac{2.8}{100} =0.028$ .
$A=P(a+rt)$
$A=8000(1+0.028*15)$
$A=11360$

In conclusion, investment A will yield a greater value than investment B at the investment period's conclusion.

3 0

26 days ago

Read 2 more answers