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9 days ago

The Changs updated their bedroom by purchasing a new lamp for $89.95 and a comforter set for $239.99. They paid 2007-03-04-00-00

_files/i0120000.jpg% sales tax on their purchases. If the Changs paid $351.72 total, determine if they paid the correct amount.

Mathematics

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Josh needs to cover a rectangular opening of 12 inches × 18 inches with plywood. how much will he need, in square feet, if he wa

tester [12383]

We understand that

1 foot corresponds to 12 inches.

Step 1

Dimensions of the plywood needed are

(12+3+3) x (18+3+3)------> 18 inches x 24 inches.

Step 2

Convert inches into feet:

18 in-------> 18/12=1.5 ft.

24 in------> 24/12=2 ft.

Step 3

To calculate the area of plywood needed:

A=b*h------> 1.5*2------> A=3 ft².

The final result is

3 ft²

5 0

2 months ago

Below is an attempt to derive the derivative of sec(x) using product rule, where x is in the domain of secx. In which step, if a

tester [12383]

The mistake is present in step 3. According to the product rule, we find

$\dfrac{\mathrm d}{\mathrm dx}(\sec x\times\cos x)=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x+\sec x\times\dfrac{\mathrm d}{\mathrm dx}(\cos x)$

$=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x\boxed{+\sec x\times(-\sin x)}$

$=\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x\boxed{-\sec x\times\sin x}$

(meaning that a factor of $\sin x$ is overlooked)

Then

$\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x-\sec x\times\sin x=0$

$\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)\times\cos x=\sec x\times\sin x$

$\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)=\dfrac{\sec x\times\sin x}{\cos x}$

$\implies\dfrac{\mathrm d}{\mathrm dx}(\sec x)=\sec x\times\tan x$

6 0

1 month ago

Archie and Veronic are located one mile (5280 ft) apart on the ground. They observe a blimp directly over the road between them.

Inessa [12570]

Answer:

The blimp's altitude is 1635.363039 feet above the ground.

Step-by-step explanation:

Archie and Veronica stand one mile (5280 ft) apart on the ground, leading to AV = 5280 feet.

Let's denote the blimp's height above ground as XB = h feet.

Archie records the angle of elevation from the ground to the blimp as 53 degrees, signifying angle ∠BAX = 53°.

Veronica, meanwhile, measures the angle of elevation to the blimp at 22 degrees, indicating angle ∠BVX = 22°.

In Right triangle ΔAXB, we utilize cot(A) = AX / XB.

Thus, AX can be expressed as AX = XB*cot(A) = h*cot(53°) = 0.75355405*h.

In Right triangle ΔVXB, cot(B) is similar: cot(B) = VX / XB.

Consequently, VX is VX = XB*cot(B) = h*cot(22°) = 2.475086853*h.

We know AV = 5280, meaning AX + VX = AV.

Therefore, AX + VX equals 5280.

From here, we can write: 0.75355405*h + 2.475086853*h = 5280.

This simplifies to: 3.228640904*h = 5280.

Thus, h is calculated as 5280 / 3.228640904 = 1635.363039 feet.

Thus, the blimp's height from the ground is 1635.363039 feet.

3 0

2 months ago

A square has a side length of 1.2 feet. If the square is dilated by a factor of 2.5, what is the length of a side of the new squ

tester [12383]

It begins at 1.2 feet. In mathematics, dilation implies resizing, thus I will provide both possible results. Confirm with your teacher the expectation of the question. For enlargement, 1.2 * 2.5 equals 3, and for reduction, 1.2 divided by 2.5 equals 0.48.

4 0

1 month ago

Peyton is three years younger than Justin. Matt is four times as old as Peyton. If you add together the ages of Justin, Peyton a

Inessa [12570]

Peyton's age is 28 years old

Justin is 7 years old

Matt has reached 4 years old

5 0

2 months ago

Read 2 more answers