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3 years ago

Miss Stoner purchase a new computer for $1,150 at the Apple store if sales tax is 7.5% what is the total of her purchase

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

4 0

Answer:

$1236.25

Step-by-step explanation:

We can convert the percentage to 0.075 to make it easier. Then, multiply 1150 by 1.075 to get 1236.25. We add the one because we need to include the initial $1150.

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A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

mr Goodwill [35]

Answer: 8.26 m

Step-by-step explanation:

$Let s be the length of the wire used for the square. \\Let $t$ be the length of the wire used for the triangle. \\Let $A_{S}$ be the area of the square. \\Let ${A}_{T}}$ be the area of the triangle. \\One side of the square is $\frac{s}{4}$ \\Therefore,we know that,$$A_{S}=\left(\frac{s}{4}\right)^{2}=\frac{s^{2}}{16}$

$The formula for the area of an equilateral triangle is, $A=\frac{\sqrt{3}}{4} a^{2}$ where $a$ is the length of one side,And one side of our triangle is $\frac{t}{3}$So,We know that,$$A_{T}=\frac{\sqrt{3}}{4}\left(\frac{t}{3}\right)^{2}$$We have to find the value of "s" such that,$\mathrm{s}+\mathrm{t}=19$ hence, $\mathrm{t}=19-\mathrm{s}$And$$A_{S}+A_{T}=A_{S+T}$

$$$Therefore,$$\begin{aligned}&A_{T}=\frac{\sqrt{3}}{4}\left(\frac{(19-s)}{3}\right)^{2}=\frac{\sqrt{3}(19-s)^{2}}{36} \\&A_{T+S}=\frac{s^{2}}{16}+\frac{\sqrt{3}(19-s)^{2}}{36}\end{aligned}$

$Differentiating the above equation with respect to s we get,$$A^{\prime}{ }_{T+S}=\frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}$$Now we solve $A_{S+T}^{\prime}=0$$$\begin{aligned}&\Rightarrow \frac{s}{8}-\frac{\sqrt{3}(19-s)}{18}=0 \\&\Rightarrow \frac{s}{8}=\frac{\sqrt{3}(19-s)}{18}\end{aligned}$$Cross multiply,$$\begin{aligned}&18 s=8 \sqrt{3}(19-s) \\&18 s=152 \sqrt{3}-8 \sqrt{3} s \\&(18+8 \sqrt{3}) s=152 \sqrt{3} \\&s=\frac{152 \sqrt{3}}{(18+8 \sqrt{3})} \approx 8.26\end{aligned}$

$The domain of $s$ is $[0,19]$.So the endpoints are 0 and 19$$\begin{aligned}&A_{T+S}(0)=\frac{0^{2}}{16}+\frac{\sqrt{3}(19-0)^{2}}{36} \approx 17.36 \\&A_{T+S}(8.26)=\frac{8.26^{2}}{16}+\frac{\sqrt{3}(19-8.26)^{2}}{36} \approx 9.81 \\&A_{T+S}(19)=\frac{19^{2}}{16}+\frac{\sqrt{3}(19-19)^{2}}{36}=22.56\end{aligned}$

$$$Therefore, for the minimum area, $8.26 \mathrm{~m}$ should be used for the square$

8 0

2 years ago

HELP ASAP PLS!!! 30 POINTS AND BRAINLEST IF UR RIGHT ANSWER ALL FOUR TO GET BRAINLEST!!!!!!

Brums [2.3K]

Answer:

C,D,A,A

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Can someone help me pls on this question pls

jekas [21]

C is the answer of this problem

3 0

3 years ago

The equation h(t) = 1.2 + 40t – 5t2 models the height, in meters of a ball t

Marina CMI [18]

Answer:

Step-by-step explanation:

To determine the time when the height is 40 meters above the ground, we would substitute 40 for h in the given equation. It becomes

1.2 + 4t0t - 5t² = 40

5t² - 40t + 40 - 1.2 = 0

5t² - 40t + 38.8 = 0

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 5

b = - 40

c = 38.8

Therefore,

t = [- - 40 ± √(- 40² - 4 × 5 × 38.8)]/2 × 5

t = [40 ± √(1600 - 776)]/10

t = [40 ± √824]/10

t = (40 + 28.71)/10 or x = (40 - 28.71)/10

t = 6.871 seconds or t = 1.129 seconds

3 0

3 years ago

Find the surface area of the prism. 13 m 5 m 11 m 12 m HELP ME ASAP

USPshnik [31]

Answer: 345.977 m^3

Step-by-step explanation:

3 0

3 years ago