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3 years ago

Whats (c-7)(c+5) , (double brackets)

Mathematics

2 answers:

kherson [118]3 years ago

6 0

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

let's evaluate :

$(c - 7)(c + 5)$

${c}^{2} + 5c - 7c - 35$

${c}^{2} - 2c - 35$

Strike441 [17]3 years ago

5 0

$\\ \sf\longmapsto (c-7)(c+5)$

$\\ \sf\longmapsto c(c+5)-7(c+5)$

$\\ \sf\longmapsto c^2+5c-7c-35$

$\\ \sf\longmapsto c^2-2c-35$

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The manufacturing engineers of a renowned pizza brand reduced the manufacturing cost of a pizza delivery box by optimising the s

jekas [21]

Given: A pizza box's volume has been reduced by 25% by flattening the curved side of the box. The dimensions of the box are given.

Required: To determine the angle, the area of the sector of the top surface of the old box design, the area of the top surface of the newly designed box, and the volume, V, of the newly designed box. Also, determine the height of the box, h.

Explanation: The given box is-

If we draw a perpendicular as shown in the figure, the angle is bisected, and the side 24 cm is also bisected as the triangle on the top is an isosceles triangle. This can be easily proved by showing that the smaller triangles on the top face are congruent.

Next, we can use the trigonometric ratio sine to determine the angle as follows-

$\begin{gathered} sin\theta=\frac{12}{36} \\ \theta=sin^{-1}(\frac{1}{3}) \\ \theta=19.47\degree \end{gathered}$

Thus,

$2\theta=38.94\degree$

Next, the top of the new box is now a triangle with a base of 24 cm and a height-

$\begin{gathered} \text{ Height of triangle}=36cos\theta \\ =36cos(19.47\degree) \\ =33.94\text{ cm} \end{gathered}$

Hence, the area is-

$\begin{gathered} A=\frac{1}{2}\times24\times33.94 \\ =407.30\text{ cm}^2 \end{gathered}$

Now, the old box is a sector with a central angle of 38.94 degrees and a radius of 36 cm. Hence the area of the old box is-

$\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}$

Substituting the values as-

$\begin{gathered} A=\frac{38.94}{360}\times3.14\times36\times36 \\ =440.18\text{ cm}^2 \end{gathered}$

Lastly, the volume of the new box is 25% less than the old box. Hence the volume of the new box is-

$\begin{gathered} V=\frac{25}{100}\times3277 \\ =819.25\text{ cm}^3 \end{gathered}$

We can determine the height as follows-

$\begin{gathered} Vol=Area\times h \\ \Rightarrow h=\frac{Vol}{Area} \end{gathered}$

Hence,

$\begin{gathered} h=\frac{819.25}{407.30} \\ =2.011\text{ cm} \end{gathered}$

Final Answer: A)

$2\theta=38.94\degree$

B) i) The area of the top of the old box=440.18 sq centimeters.

ii) The area of the top of the new box=407.30 sq centimeters.

C) i) The volume of the new box is 819 cubic centimeters.

ii) h=2.01 cm

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2 years ago

F(x)=0.5x^2-2 and g(x)=8x^3+2

BARSIC [14]

Answer:

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

Step-by-step explanation:

To find (f*g)(x), you need to multiply f(x) with g(x). Use FOIL to multiply.

f(x) = 0.5x² - 2

g(x) = 8x³ + 2

(f*g)(x) = (0.5x² - 2)(8x³ + 2)

(f*g)(x) = 4x⁵ + x² - 16x³ - 4

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3 years ago

URGENT: Find the x- and y-intercepts of the graph of y = 14x − 2

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frez [133]

Answer:

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Step-by-step explanation:

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3 years ago

The following set of points belong to a specific function: {(-3,15)(-2,17), (-1,11), (0,3),(1,-1), (2,5),(3,27)} Based on the se

adelina 88 [10]

Answer:

(a)Degree 3

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Step-by-step explanation:

The function represented by the set of points: {(-3,15)(-2,17), (-1,11), (0,3),(1,-1), (2,5),(3,27)} has 2 turning points when plotted on a graph.

(a)Now, we know that the maximum number of turning points of a polynomial function is always one less than the degree of the function.

Therefore, the polynomial has a degree of 3

(b)A cubic function is one in the form $f(x)=ax^3+bx^2+cx+d .$ where d is the y-intercept.

From the set of values, the y-intercept, d=3

Therefore, our polynomial is of the form:

$f(x)=ax^3+bx^2+cx+3 .$

$\text{At } (-3,15), 15=a(-3)^3+b(-3)^2+c(-3)+3 \implies -27a+9b-3c=12\\\text{At } (-2,17), 17=a(-2)^3+b(-2)^2+c(-2)+3 \implies -8a+4b-2c=14\\\text{At } (-1,11), 11=a(-1)^3+b(-1)^2+c(-1)+3 \implies -a+b-c=8$

Solving the three resulting equations simultaneously use a calculator), we obtain:

$a=1, b=2, c=-7$

Therefore, an equation of this function is:

$f(x)=x^3+2x^2-7x+3 .$

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3 years ago